Consider the vector space V = C² with scalar multiplication over the real numbers R (note that V is a vector space of dimension 4 over R). Let T: V→ V be the linear operator defined by T(Z₁, Z2)= (Z₁-Z₁, iZ₁ + Z₂). Use the Diagonalisability Test to explain whether T is diagonalisable over R. If T is diagonalisable, find a basis for V such that [7] is a diagonal matrix and write down [7]a- α

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